An Adaptive Sequential Procedure for Efficient Optimization of the Sheet Metal Spinning Process

Abstract

Due to technological advances in science, the complexity of processes under investigation increased continuously in recent years. For example, in mechanical engineering, there are often highly nonlinear input-output relationships combined with a large number of constraints. Sheet metal spinning is one example of such a production process. Many flexible and powerful methods to global optimization have been developed. In this paper, a sequential approach originally developed for computer experiments will be adopted and applied to optimize the spinning process based on physical experiments. This approach sequentially refines the model by adding new design points based on the expected improvement criterion. This criterion balances the need to observe at the predicted optimum with the need to investigate the design space in areas of high uncertainty. However to guarantee an efficient optimization of the spinning process, this approach has to be embedded in a more substantial procedure. One reason for this is the liability of workpiece failure for most of the operable design space. Since the shape of the failure region is unknown, many missing observations have to be expected when exploring the design space. The other reason is the need to incorporate available process knowledge of sheet metal spinning to improve the efficiency in optimization. The main problem in implementing this information is a changing process behavior for different geometries and materials used. Hence, if a component with a new geometry has to be optimized, it is difficult to include available process knowledge. In this paper, an adaptive sequential optimization procedure (ASOP) is presented to cope with these problems in order to guarantee an efficient optimization of such complex processes. The approach is exemplified by optimizing the spinning process for a fixed geometry.

Parametric toolpath design in metal spinning

“…Auer et al [7] defined a window of toolpaths that avoid wrinkling, and optimised them to minimise thinning. This led to an offline toolpath planning algorithm [8] which is practical, but limited to the parameter region of the trials. Therefore, in this work, a set of experiments is performed with a parameterised toolpath to explore how the design of the toolpath influences product geometry, tool forces, and the various failure criteria which define the operating window of spinning.…”

Discrete mixtures of kernels for Kriging‐based optimization

“…EGO has been found to be a competitive global optimization algorithm, in particular in the fields of automotive and aerospace engineering, with objective functions having one to six inputs (see ([4]), ( [7])). In other respects, ( [8]) proposes a adaptation of EGO for physical experiments.…”

“…Right: evolution of both sequences of log-weights (lower graphic), and the associated series of likelihood ratios (upper graphic). 8 …”

An Efficient Sequential Optimization Approach Based on the Multivariate Expected Improvement Criterion

“…Figure 11 gives a schematic view of this process, see also Henkenjohann et al (2005). A sheet metal is fixed to a rotating mandrel.…”

“…The weighting of the responses given by the expert is listed in Table 3. To reduce the number of workpiece failures an algorithm was developed which sequentially generates a space filling design, see Henkenjohann et al (2005). The algorithm uses the fact that the stable region is convex and excludes those parts of the design space which have already been identified to be part of the failure region.…”